A method for controlling chaos of PMSM integrated with sliding mode observer

Abstract

The application belongs to the technical field of nonlinear control of permanent magnet synchronous motor, and particularly discloses a PMSM chaos control method integrated with a sliding mode observer, which comprises the following steps: establishing a dimensionless chaos model and a TS fuzzy model of PMSM; designing a sliding mode observer based on the TS model to reconstruct unmeasurable states; designing a fuzzy adaptive sliding mode controller to constitute a feedback stable loop; designing an iterative learning controller as a feedforward learning loop to learn repeatable residual errors in a limited time domain and generate a feedforward compensation; and superimposing the feedback and the current feedforward on the motor in each iteration, updating the feedforward after the iteration, and running step by step until the error meets the requirements. The application can effectively suppress chaos oscillation under the condition of incomplete state measurement, has small chattering, fast convergence and strong robustness, and is suitable for industrial driving occasions with repeated operation.

Description

Technical Field

[0001] This invention belongs to the field of nonlinear control technology for permanent magnet synchronous motors, specifically relating to a chaotic control method for PMSM (Permanent Magnet Synchronous Motor) with an integrated sliding mode observer. Background Technology

[0002] Permanent magnet synchronous motors (MSMs) are widely used in high-precision drive applications such as CNC machine tools, industrial robots, electric vehicles, and aerospace servo systems due to their advantages of high efficiency, high power density, and fast dynamic response. However, PMSMs are inherently multivariable, strongly coupled nonlinear systems, which can exhibit chaotic oscillations under specific parameter conditions or operating conditions. Chaotic behavior leads to irregular oscillations in motor speed, current, and electromagnetic torque, resulting in decreased control accuracy, increased additional vibration and energy loss, and in severe cases, even system instability, threatening equipment safety.

[0003] To suppress chaotic oscillations in PMSM (Programmable Mode Streaming System), researchers have proposed various control strategies. Among them, sliding mode control has attracted widespread attention due to its strong robustness to parameter perturbations and external disturbances. However, traditional sliding mode control inherently suffers from high-frequency chattering, which not only affects control accuracy but may also excite unmodeled dynamics in the system, leading to actuator wear. To suppress chattering, researchers have introduced mechanisms such as fuzzy logic and adaptive adjustment, forming methods such as fuzzy adaptive sliding mode control. However, fuzzy adaptive sliding mode control is essentially an error-driven feedback compensation mechanism, and its control action only starts after chaotic oscillations or disturbances occur. It has an inherent lag for periodic disturbances and repetitive errors, making it difficult to achieve active feedforward compensation, thus limiting further improvements in control accuracy and convergence speed.

[0004] On the other hand, iterative learning control is suitable for tasks that run repeatedly within a finite time interval, and can generate feedforward compensation using historical error information to gradually improve system performance. However, existing iterative learning control methods usually learn directly from open chaotic orbits, facing problems of orbit instability and difficulty in guaranteeing convergence in chaotic systems. In addition, most existing PMSM chaotic control studies assume that the system state is completely measurable. However, in practical engineering, due to limitations in cost, installation space, and sensor accuracy, key states such as rotor angular velocity and some currents are often difficult to measure directly or accurately, which seriously restricts the engineering practicality of advanced control strategies. Summary of the Invention

[0005] The purpose of this invention is to solve the problem of insufficient PMSM chaos suppression capability under uncertain parameter conditions, and to propose a PMSM chaos control method with integrated sliding mode observer.

[0006] The technical solution of this invention is: a PMSM chaotic control method integrating a sliding mode observer is provided, comprising: Step 1: Establish a dimensionless chaotic dynamic model of the permanent magnet synchronous motor, construct a TS fuzzy model under parameter uncertainty based on the dimensionless chaotic dynamic model, and define the expected equilibrium point of the PMSM chaotic system; Step 2: Design a sliding mode observer based on the TS fuzzy model. The sliding mode observer is used to reconstruct the unmeasurable state variables online using the measurable output of the permanent magnet synchronous motor to obtain the state estimate. Step 3: Based on the TS fuzzy model, design a fuzzy adaptive sliding mode controller to form a feedback stabilization loop and a closed-loop system. The fuzzy adaptive sliding mode controller is used to generate feedback control quantity to suppress non-repetitive disturbances based on the state error calculated from the state estimate and the desired equilibrium point. Step 4: Design an iterative learning controller to form a feedforward control loop, so as to learn the repeatable residual error of the closed-loop system in the finite time domain during one iteration and generate the feedforward compensation quantity. Step 5: During each iteration, the feedback control quantity output by the fuzzy adaptive sliding mode controller is superimposed with the feedforward compensation quantity provided by the iterative learning controller for the current iteration to form a total control input applied to the permanent magnet synchronous motor. Step 6: After each iteration, using the tracking error of the current iteration, update the feedforward compensation amount for the next iteration according to the update law of the iterative learning controller, and enter the next iteration. Repeat steps 5 to 6 until the tracking error meets the preset accuracy requirements.

[0007] Preferably, step 1 includes: Step 1.1: Establish a dimensionless chaotic dynamic model of the permanent magnet synchronous motor in the dq-axis coordinate system; Step 1.2: Using the state variables of the permanent magnet synchronous motor as fuzzy antecedents, set the fuzzy set and membership function, represent the dimensionless chaotic dynamics model as a weighted combination of several local linear subsystems, and introduce internal parameter disturbances and bounded external disturbances to obtain the TS fuzzy model, and define the desired equilibrium point of the PMSM chaotic system.

[0008] Preferably, the TS fuzzy model is represented as follows: ; in, Let be the system state vector. For the system's control input, For the first The state matrix corresponding to the fuzzy rules, For the input matrix, For the parameter uncertainty term, For a bounded external disturbance, satisfying , This represents the upper bound function of the perturbation. Indicates time, This is the normalized membership function.

[0009] Preferably, step 2, which involves designing a sliding mode observer, includes: S11: Construct a sliding mode observer structure corresponding to the fuzzy rules of the TS fuzzy model, expressed as: ; in, This is the state estimate. Let be the input vector of the system, and let be the first... The state matrix corresponding to the fuzzy rules, For the input matrix, Indicates time, For the normalized membership function, For fuzzy reasoning input, It is the first i The linear observer gain matrix corresponding to the fuzzy rule. For system output, To output the estimated value, For the first i The sliding switch item corresponding to the fuzzy rule; S12: Define the state estimation error and determine the dynamic equation of the state estimation error based on the TS fuzzy model and the sliding mode observer structure; S13: Construct a sliding surface based on the output estimation error, and design a sliding mode switching term based on the sliding surface to suppress observer chattering.

[0010] As a preferred option, the first i The sliding switch term corresponding to each fuzzy rule is represented as:

[0011] In the formula, To switch the gain, a matrix is ​​designed for the sliding surface. For the output matrix, It is a positive definite matrix. Boundary layer thickness, It is a sliding surface.

[0012] Preferably, step 3, which involves designing a fuzzy adaptive sliding mode controller, includes: S21: The fractional-order sliding surface is designed as follows: ; in, It is a fractional-order sliding surface. For time, For rotor angular velocity error, For d-axis current error, For q-axis current error, The fractional-order gain coefficient, The linear gain coefficient, and , It is a fractional power, and ; S22: Design a control law based on the fractional-order sliding surface. The control law is expressed as follows: ; In the formula, This is an equivalent control law. To switch control laws; The equivalent control law is expressed as follows: ; In the formula, For system state-related functions; The switching control law is expressed as follows: ; In the formula, To switch gain, It is a fractional-order sliding surface. It is a saturation function. For boundary thickness; S23: A fuzzy logic system is used to adjust the switching gain of the switching control law in real time to achieve adaptive chattering suppression.

[0013] Preferably, the method for updating the switching gain is as follows: ; In the formula, Based on the gain, The switching gain adjustment amount is the output of the fuzzy logic system. For fuzzy output scaling factor, For adaptive learning rate, For, a fractional-order sliding surface.

[0014] Preferably, the iterative learning controller designed in step 4 includes: S31: The weighted tracking error is constructed as follows: ; In the formula, For weighted tracking error, For the number of iterations, For time, The rotor angular velocity, For d-axis current, For q-axis current, This is the weighting coefficient for the rotor angular velocity. This is the weighting factor for the d-axis current. This is the weighting coefficient for the q-axis current; S32: Design the update law of the iterative learning controller based on the weighted tracking error, the update law being expressed as: ; In the formula, For the first Feedforward compensation amount in the next iteration. For learning rate, For the derivative term of the weighted tracking error, This is the gain coefficient. For the first The memory information of the next iteration This is an amplitude limiting function. These are the weighting coefficients. For the axis current.

[0015] Preferably, the learning rate An adaptive mechanism is used, which is expressed as: ; In the formula, Based on learning rate decay, The value varies with the number of iterations The increase is monotonically decreasing. As the error trend factor, The value is adjusted in real time based on the changing trend of the weighted tracking error within a preset short time window. This is the weighted tracking error.

[0016] Preferably, the maximum allowable amplitude of the amplitude limiting function varies with the number of iterations. Gradual relaxation is represented as: ; In the formula, This indicates the upper limit of the maximum allowable amplitude of the feedforward compensation.

[0017] The beneficial effects of this invention are: The PMSM chaotic control method of the integrated sliding mode observer of the present invention is based on T The sliding mode observer designed using the S-fuzzy model can quickly and accurately estimate unmeasurable states under parameter uncertainty and bounded disturbances, and simultaneously use the estimated values ​​for feedback control and iterative learning. This design reduces the system's dependence on physical sensors, improves engineering economy and reliability, and makes the invention applicable to practical operating conditions where states are not fully measurable. Through the sliding mode observer's ability to suppress lumped uncertainty terms, the online estimation of the disturbance upper bound of the fuzzy adaptive sliding mode controller, and the learning compensation for repetitive disturbances by iterative learning control, the system maintains excellent stability and consistency even under complex operating conditions involving parameter perturbations, external disturbances, and measurement noise. Attached Figure Description

[0018] Figure 1 The flowchart shown is a PMSM chaotic control method with an integrated sliding mode observer. Figure 2 The diagram shown is a flowchart of the PMSM chaotic control process with an integrated sliding mode observer. Figure 3 The figure shown is the phase trajectory diagram of a chaotic system of a permanent magnet synchronous motor. Figure 4 The diagram shown is a fuzzy control flowchart. Figure 5 The figure shown is a comparison between the state estimate and the true value of the rotor angular velocity of the sliding mode observer; Figure 6 The figure shown is a comparison between the state estimate and the true value of the d-axis current of the sliding mode observer; Figure 7 The figure shown is a comparison of the rotor angular velocity response of the method of the present invention under white noise interference; Figure 8 The figure shown is a comparison of the d-axis current response of the method of the present invention under white noise interference; Figure 9 The figure shown is a comparison of the response of the q-axis current of the method of the present invention under white noise interference; Figure 10 The figure shown is a comparison of the time-domain response of the rotor angular velocity under three control configurations; Figure 11 The figure shows a comparison of the time-domain response of the q-axis current under three control configurations; Figure 12 The figure shows a comparison of the time-domain response of the d-axis current under three control configurations; Figure 13 The figure shows a comparison of the time-domain response of the control input under three control configurations. Detailed Implementation

[0019] Exemplary embodiments of the present invention will now be described in detail with reference to the accompanying drawings. It should be understood that the embodiments shown and described in the drawings are merely exemplary and are intended to illustrate the principles and spirit of the invention, and are not intended to limit the scope of the invention.

[0020] This invention provides a PMSM chaotic control method with an integrated sliding mode observer. Please refer to [link to previous document]. Figure 1 and Figure 2 , Figure 1 The flowchart shown is a PMSM chaotic control method with an integrated sliding mode observer. Figure 2 The diagram shown is a flowchart of the PMSM chaotic control process with an integrated sliding mode observer.

[0021] like Figure 1 As shown, the PMSM chaos control method with an integrated sliding mode observer in this embodiment includes the following steps: Step 1: Establish a dimensionless chaotic dynamic model of the permanent magnet synchronous motor, construct a TS fuzzy model under parameter uncertainty based on the dimensionless chaotic dynamic model, and define the expected equilibrium point of the PMSM chaotic system.

[0022] In this embodiment, step 1 includes: Step 1.1: Establish a dimensionless chaotic dynamic model of the permanent magnet synchronous motor in the dq axis coordinate system.

[0023] In this embodiment, the dimensionless chaotic dynamics model can be expressed as: ; In the formula, The rate of change of rotor angular velocity, Let be the rate of change of the d-axis current. Let be the rate of change of the q-axis current. These are system parameters, typically control or gain coefficients. These are system parameters, typically representing the coupling strength between the rotor and the current. The rotor angular velocity, For d-axis current, This is the q-axis current.

[0024] When the permanent magnet synchronous motor is de-energized and there is no external input, the initial parameters for the dimensionless chaotic dynamics model are selected as follows: ( , , ) = (33, -8, -11). =5.46, using the Matlab simulation system with varying parameters The dynamic response under changing conditions is shown in the simulation results. Figure 3 . Figure 3The figure shows the phase trajectory diagram of a chaotic system of a permanent magnet synchronous motor, where (a) is the phase trajectory diagram of the system. The phase trajectory diagram of the system with =5 is shown in Figure (b). Phase trajectory diagram of system =15, (c) figure Phase trajectory diagram of the system with a value of 25.

[0025] As can be seen from the figure, when The system remains stable at smaller values, exhibiting slight oscillations in the initial response that decay over time. With... Increasing the value to 15 indicates that the system has entered a chaotic state, with phase trajectories exhibiting chaotic attractors and state variables beginning to change irregularly. When the value is further increased to 25, the chaotic behavior is fully developed, a clear chaotic attractor is formed in the phase space, and each state variable exhibits highly nonlinear continuous oscillations. The results show that PMSMs can exhibit complex behaviors such as chaos and periodic motion under specific parameter conditions. This chaotic phenomenon not only disrupts the stability of motor operation but also poses a potential threat to motor safety.

[0026] Step 1.2: Using the state variables of the permanent magnet synchronous motor as fuzzy antecedents, set the fuzzy set and membership function, represent the dimensionless chaotic dynamics model as a weighted combination of several local linear subsystems, and introduce internal parameter disturbances and bounded external disturbances to obtain the TS fuzzy model, and define the desired equilibrium point of the PMSM chaotic system.

[0027] In this embodiment, the TS fuzzy model is represented as: ; in, Let be the system state vector. The input vector of the system, For the first The state matrix corresponding to the fuzzy rules, For the input matrix, For the parameter uncertainty term, For a bounded external disturbance, satisfying , This represents the upper bound function of the perturbation, which is related to time. Related, Indicates time, This is the normalized membership function.

[0028] The TS fuzzy model is an effective tool for modeling dynamic systems. Its core idea is to decompose a complex nonlinear system into multiple locally linear subsystems, with each fuzzy rule describing the system's dynamic characteristics within a specific input range. The output of each fuzzy rule is a linear equation whose coefficients depend on the input variables. By weighting and fusing these linear outputs through fuzzy membership functions, the global dynamic behavior of the original system can be approximated, thus providing support for controller design.

[0029] Specifically, for a dimensionless chaotic dynamics model, the state variables are assumed to be... , When the system is in a chaotic state, Its amplitude range is approximately [-25, 30], but its main energy is concentrated in the interval [-10, 10]. The fuzzy rule expression for this system, which covers the main dynamic range, is as follows: ; in , and This is the membership function.

[0030] ; In fuzzy modeling methods, variables Defined as a fuzzy antecedent. Assign it a set of fuzzy sets. These fuzzy sets must satisfy the following conditions: the membership function values ​​of each set are non-negative, and the sum of all membership function values ​​at any given time is 1. Within this framework, the chaotic system of PMSM can be transformed into a fuzzy model for description: .

[0031] In this embodiment, to make the PMSM model more consistent with reality, two types of uncertainty are designed: first, the internal parameters of the system may have random disturbances of up to 10%; second, external disturbances. Bounded, satisfied .

[0032] Based on this, a TS fuzzy model of a chaotic system under parameter uncertainty is established. The parameter-uncertain PMSM chaotic system based on the TS model can then be represented as: ; The uncertain term satisfies: ; In the formula, Let be the system state vector. For the system's control input, For the first The state matrix corresponding to the fuzzy rules, For the first The input matrix corresponding to the fuzzy rules and For the parameter uncertainty term, For time-dependent normalized matrices, It is a diagonal matrix. It is the identity matrix. and The state matrix, For the first fuzzy rule regarding external disturbances, This is for the second fuzzy rule regarding external disturbances.

[0033] To ensure the system meets controllable matching conditions, select Under these conditions, the TS fuzzy model of the chaotic system under parameter uncertainty can be obtained.

[0034] In this embodiment, the desired equilibrium point of the PMSM chaotic system is defined as... The control objective is to stabilize the system to the desired equilibrium point.

[0035] Step 2: Design a sliding mode observer based on the TS fuzzy model. The sliding mode observer is used to reconstruct the unmeasurable state variables online using the measurable output of the permanent magnet synchronous motor to obtain the state estimate.

[0036] The Sliding Mode Observer (SMO), a state estimation method based on sliding mode variable structure theory, shares the same core idea as sliding mode control. Both methods introduce a discontinuous feedback term to force the system's state estimation error to converge to a pre-designed sliding surface within a finite time, and then maintain motion on that surface. Once the system enters sliding mode motion, its dynamic characteristics are determined by the sliding surface, thus exhibiting strong robustness to parameter perturbations and external disturbances.

[0037] In this embodiment, the design of the sliding mode observer includes the following steps: S11: Construct the sliding mode observer structure corresponding to the fuzzy rules of the TS fuzzy model, expressed as: ; in, This is the state estimate. The input vector of the system, For the first The state matrix corresponding to the fuzzy rules, For the input matrix, Indicates time, For the normalized membership function, For fuzzy reasoning input, It is the first iThe linear observer gain matrix corresponding to the fuzzy rule. For system output, To output the estimated value, For the first i The sliding switch item corresponding to the fuzzy rule.

[0038] It should be noted that in this embodiment, for the TS fuzzy model, it is assumed that the system output consists of partial state variables. For example, in practical applications, only a portion of the current may be measured, or indirect state information may be obtained through certain sensors. For generality, the output equation is assumed to be: .in, The output matrix is, and If all states are measurable, then This embodiment considers This is a situation where the state is not fully measurable.

[0039] Specifically, based on the TS fuzzy model representation, the following sliding mode observer based on the TS fuzzy model is designed: Observer Rules i ( ): IF is THEN

[0040] END IF in, It is a state The estimated value, It is an estimated value of the output. It is the first The linear observer gain matrix corresponding to each rule is used to improve the dynamic performance of the estimation error before the sliding mode motion occurs. It is the first The sliding mode switching term corresponding to each rule is used to ensure the robustness of the estimation error to uncertainties and disturbances. A global sliding mode observer is obtained using fuzzy inference.

[0041] S12: Define the state estimation error and determine the dynamic equation of the state estimation error based on the TS fuzzy model and sliding mode observer structure.

[0042] The fundamental purpose of sliding mode observer design is to make the state estimate... To get as close as possible to the real state The degree of approximation is directly determined by the state estimation error. This is used to measure the error. Therefore, the ultimate goal of observer design is to minimize the state estimation error. It should be zero or as small as possible.

[0043] Define the state estimation error as: ; By differentiating the state estimation error and substituting the original system dynamics and the observer dynamics, we can obtain the dynamic equation for the state estimation error:

[0044] make Then the error dynamic equation simplifies to: ; in, This represents the uncertainty and disturbance term in the lumped set. Because... Bounded and Bounded, assumption It is bounded, meaning it has positive constants. Make: ; S13: Construct a sliding surface based on the output estimation error, and design a sliding mode switching term based on the sliding surface to suppress observer chattering.

[0045] Specifically, no. i The sliding switch term corresponding to each fuzzy rule is represented as: ; In the formula, To switch the gain, Design a matrix for the synovial surface. For the output matrix, It is a positive definite matrix. Boundary layer thickness, It is a sliding surface.

[0046] Specifically, the performance of a sliding mode observer hinges on the design of the sliding surface. The sliding surface is designed based on the output estimation error: ; in, It is a non-singular design matrix used to adjust the properties of the sliding surface. Typically, for simplicity, it can be taken as... The goal of sliding mode control is to design switching items. This drives the system trajectory to reach and maintain the sliding surface within a finite time. Above. To the sliding surface To ensure sliding mode motion occurs, the sliding mode reachability condition must be satisfied. Therefore, the Lyapunov direct method is used for design. Candidate Lyapunov functions are selected as follows:

[0047] right Differentiate: ; To force the system trajectory to tend toward the sliding surface, it is necessary to ensure when Thus, the switching item was designed.

[0048] Understandably, in standard SMO designs, gain is often used to... To stabilize And let Mainly deals with uncertainties To enhance performance, it can be designed... for: .in Used for partial compensation However, this complicates the observer structure. A more common and robust approach is to assume linear gain. It has already made It is Hurwitz's, therefore The impact can be covered by robust terms. In this embodiment, the latter approach is adopted.

[0049] In the synovial switching item of this embodiment, It is the switching gain, the magnitude of which needs to be greater than the uncertainty term. The upper bound under a certain norm. It is a symmetric positive definite matrix ( It is usually obtained by solving the Lyapunov equations of the observer, and its introduction is to construct a weighted norm in the proof, thereby increasing the degree of freedom of the design. It is a small positive constant used in When the signal approaches zero, a boundary layer is introduced to smooth the discontinuous switching function into a continuous saturation function, thereby effectively suppressing chattering in the observer output.

[0050] Step 3: Based on the TS fuzzy model, design a fuzzy adaptive sliding mode controller to form a feedback stabilization loop and create a closed-loop system. The fuzzy adaptive sliding mode controller is used to generate feedback control quantity to suppress non-repetitive disturbances based on the state error calculated from the state estimate and the desired equilibrium point.

[0051] Sliding mode control is a type of nonlinear control strategy that dynamically adjusts the structural characteristics of the system based on its real-time state, driving the system to move along a predetermined trajectory to achieve the control objective. Sliding mode dynamics can be designed as needed and has a certain degree of suppression against small changes in system parameters and external disturbances, thus exhibiting good robustness. The core of sliding mode control lies in changing the controller structure in real time according to the current system state to achieve the desired dynamic performance.

[0052] First, the principle and design method of sliding mode control are explained. The state space is switched by the surface. Divided into and In two regions, the motion of a state point within the neighborhood of the hyperplane manifests in three modes: crossing (the state point crosses the switching surface and reaches the other side), moving away (the state trajectory deviates from the hyperplane from both sides when approaching it), and approaching (the state trajectory asymptotically converges to the switching surface). If a hyperplane can attract the state trajectory to asymptotically approach it, then the hyperplane is called a sliding mode surface. Once the state point reaches the sliding mode surface, its subsequent motion is the sliding mode.

[0053] Sliding mode control is an effective control method for handling complex nonlinear systems, typically involving two steps. First, a sliding mode switching function is designed to guide the system into a sliding mode and stabilize it at the control objective. This step determines the system's dynamic response characteristics. Second, a sliding mode controller is designed to make the system state approach the sliding surface along a predetermined trajectory and maintain sliding. The choice of the sliding surface is crucial to system performance; a reasonable sliding surface and control law design can achieve fast and accurate control of nonlinear systems.

[0054] In this embodiment, a fuzzy adaptive sliding mode controller is designed, including the following steps: S21: The fractional-order sliding surface is designed as follows: ; in, It is a fractional-order sliding surface. For time, For rotor angular velocity error, For d-axis current error, For q-axis current error, The fractional-order gain coefficient controls the intensity of the nonlinear term's influence. The linear gain coefficient, and , It is a fractional power, and ; S22: The control law is designed based on the fractional-order sliding surface. The control law is expressed as follows: ; In the formula, This is an equivalent control law. To switch control laws.

[0055] In this embodiment, the equivalent control law is expressed as: ; In the formula, This is a system state-related function.

[0056] In this embodiment, the switching control law is expressed as: ; In the formula, To switch gain, It is a fractional-order sliding surface. This is a saturation function used to limit the switching amount and reduce chattering. For boundary thickness; Specifically, the tracking error is first clearly defined. Let the control objective be stabilization to the equilibrium point. ,but , , To achieve finite-time convergence and improve dynamic performance, a fractional-order sliding surface is designed. To ensure the system satisfies the TS fuzzy model, a Lyapunov function is constructed: ; in, The upper bound of the unknown perturbation. Its estimated value, For adaptive gain.

[0057] After differentiating the fractional-order sliding surface and rearranging it according to the nominal and input terms, we get: ; in: ; .

[0058] In order to make satisfy: The control law is designed as follows: Let the nominal system (undisturbed d=0) ,So, ; The equivalent control law can be obtained from the above formula. .

[0059] S23: A fuzzy logic system is used to adjust the switching gain of the switching control law in real time to achieve adaptive chattering suppression.

[0060] In this embodiment, the gain update method is as follows: ; In the formula, Based on the gain, The switching gain adjustment amount is the output of the fuzzy logic system. For fuzzy output scaling factor, For adaptive learning rate, It is a fractional-order sliding surface.

[0061] Understandably, to maintain the robustness of sliding mode control and suppress chattering, fuzzy logic control is introduced to construct a fuzzy adaptive sliding mode controller (FASMC). This controller retains the framework of an adaptive sliding mode controller and dynamically adjusts the switching gain or smoothing switching function of the switching control law through a fuzzy logic system, thereby achieving the dual objectives of vibration suppression and performance optimization.

[0062] Please see Figure 4 , Figure 4 The diagram shown is a fuzzy control flowchart. Figure 4 As shown, fuzzy control is an intelligent control method based on fuzzy set theory. Its core structure includes four modules: fuzzification, knowledge base, fuzzy inference, and defuzzification. It can simulate the human experience-based decision-making process. Fuzzy control first transforms the precise input quantity into a fuzzy quantity over the fuzzy domain through the fuzzification module. Then, the fuzzy inference engine, based on expert experience stored in the knowledge base, matches the fuzzy input with rules to obtain a fuzzy output vector. This fuzzy result needs to be processed by the defuzzification module to be transformed into a precise quantity before it can be used as the final control command to drive the controlled object.

[0063] In practical applications of sliding mode variable structure control systems, due to the ideal switching function Difficult to achieve under conditions of time and space lag often leads to frequent traversals of the system state near the sliding surface, resulting in chattering. This chattering not only reduces the system's control accuracy and dynamic performance but can also cause mechanical damage to the actuators in severe cases. To effectively suppress chattering and improve the control effect of sliding mode control in a chaotic permanent magnet synchronous motor system, a fuzzy control strategy is introduced in this embodiment to smooth the original switching function in the sliding mode control. By designing an adaptive gain switching mechanism, the system can automatically adjust the gain value according to the magnitude of external disturbances: a higher gain is used when the disturbance is large to ensure the system's robustness; a lower gain is used when the disturbance is small, thereby effectively reducing chattering.

[0064] For the control law in this embodiment Equivalent control law Used to maintain the system's motion on the sliding surface, switching control laws. Used to overcome uncertainties and disturbances. To adaptively adjust the switching gain. A fuzzy logic system is introduced. The input to the fuzzy system is the sliding surface. and sliding surface change rate The output is the adjustment amount for switching gain. The control quantity required for final control is derived using fuzzy rule reasoning. This is a necessary condition for the existence of a sliding mode; when this condition is met, It should be smaller, that is ;like , It should be larger, that is This design ensures that the system can quickly converge to the sliding surface when there are uncertainties and disturbances, and can reduce chattering by adaptively adjusting the gain and saturation function.

[0065] The result obtained from fuzzy inference is transformed into the precise output value of the fuzzy controller: ; In the formula, These are the weighting coefficients for the equivalent control output, used to represent the contribution of the equivalent control output to the fuzzy control output. To switch control outputs, thereby enhancing the controller's ability to cope with uncertainties and disturbances. These are weighting coefficients used for hybrid equivalent control and switching control to smooth the control output and reduce chattering. The weighting coefficients for switching control outputs.

[0066] When the system is not disturbed by external factors When there is an external disturbance, the controller only contains the equivalent control term; however, when there is an external disturbance... In this case, the controller consists of an equivalent control term and a switching term. By introducing a fuzzy controller to smooth the switching term, chattering can be significantly reduced while effectively suppressing interference.

[0067] Step 4: Design an iterative learning controller to form a feedforward control loop, so as to learn the repeatable residual error of the closed-loop system in the finite time domain during one iteration and generate the feedforward compensation quantity.

[0068] Understandably, the control strategy combining the fractional-order sliding surface of the fuzzy adaptive sliding mode controller with an adaptive law can estimate the upper bound of disturbances online without relying on prior information about the disturbance. When facing internal parameter perturbations and external sinusoidal disturbances, it can effectively suppress chaotic oscillations and bring the system state to converge to a small neighborhood near the equilibrium point, exhibiting good robustness and dynamic adjustment capability. The fuzzy adaptive sliding mode controller is essentially an error-driven feedback compensation mechanism. Its control action only activates after chaotic oscillations or external disturbances have occurred and caused the system state to deviate from the equilibrium point. This control mode has good robustness to random, non-periodic uncertainties, but it exhibits inherent hysteresis when dealing with the repeatable components of the closed-loop residual error in PMSM operation.

[0069] Therefore, when facing periodic or repetitive tasks, there is a need to find an intelligent control mechanism that can go beyond simple feedback and has the ability to actively predict and feedforward compensate. In this embodiment, an Iterative Learning Control (ILC) is designed, which can use the system's historical operating data to autonomously learn and generate effective feedforward compensation, thereby canceling out periodic disturbances before they occur, reducing the dependence on feedback control at the root, and further suppressing chattering.

[0070] In this embodiment, the core of ILC lies in learning from the error (i.e., tracking error) in each iteration and adjusting the control input so that the system output gradually approaches the reference trajectory. The goal of ILC is to solve for the desired control input sequence. This causes the system to output... Within a limited time interval Internal precise tracking reference trajectory Its basic principle is based on the tracking error of the current iteration. To correct the control input for the next iteration Through repeated iterations, the system output is improved. Gradually converges to the reference trajectory .

[0071] In this embodiment, the iterative learning controller is designed, including the following steps: S31: The weighted tracking error is constructed as follows: ; In the formula, For weighted tracking error, For the number of iterations, For time, The rotor angular velocity, For d-axis current, For q-axis current, This is the weighting coefficient for the rotor angular velocity. This is the weighting coefficient for the d-axis current. This is the weighting coefficient for the q-axis current.

[0072] Since directly using the Euclidean norm of the state vector or the error of a single state may not accurately capture the relative importance of different state variables in chaos suppression in the PMSM, a weighted tracking error is designed in this embodiment, which incorporates the rotor angular velocity... d-axis current q-axis current The error information is fused into a scalar signal, which serves as the basis for learning. Wherein: Indicates the time of the last iteration.t The state trajectory. These are time-varying weighting coefficients, and their selection is not fixed but adaptively adjusted according to the iteration process and the dynamic characteristics of the system.

[0073] S32: The update law for an iterative learning controller based on weighted tracking error is expressed as: ; In the formula, For the first Feedforward compensation amount in the next iteration. For learning rate, For the derivative term of the weighted tracking error, is the gain coefficient, and is the th The memory information of the next iteration This is an amplitude limiting function. These are weighting coefficients used to adjust the influence of the d-axis current on the feedforward compensation amount. This represents the d-axis current.

[0074] In this embodiment, The proportional learning term is the core component of ILC, directly using the weighted error from the previous iteration to correct the current control input. If the previous error was at time [time value missing]... t If the system has a positive error, then a positive control correction will be applied at the same time to offset it.

[0075] A fixed learning rate makes it difficult to strike a balance between rapid convergence and stable learning. An excessively large learning rate may cause the iterative process to diverge, especially in the early stages of learning; an excessively small learning rate will lead to slow convergence. Therefore, in this embodiment, an adaptive learning rate mechanism is designed.

[0076] Specifically, learning rate An adaptive mechanism is used, which is expressed as: ; In the formula, Based on learning rate decay, The value varies with the number of iterations The increase is monotonically decreasing. As the error trend factor, For weighted tracking error, The value is adjusted in real time based on the changing trend of the weighted tracking error within a preset short time window. For example, By analyzing the five most recent sampling points within a short time window The value is used to calculate the trend of error change, which is used to dynamically adjust the iterative learning rate, so that the controller can respond quickly and prevent oscillation or overshoot.

[0077] In this embodiment, This is the differential learning term. The proportional term reflects the current state of the error, while the differential term reflects the trend of error change. Introducing the derivative information of the error can give ILC a certain degree of predictability, thereby improving the dynamic response. In practical discrete-time systems, the error derivative is approximated using the central difference method: ,in The sampling period.

[0078] In this embodiment, For memory-based learning, a memory mechanism is introduced to enhance the coherence of learning and its focus on key states. Specifically: ; It is a scalar memory variable that accumulates historical weighted error information. The forgetting factor takes values ​​of A value less than 1 indicates that the memory gradually decays over time. This prevents outdated or potentially inapplicable historical information from excessively influencing current learning, ensuring the real-time updating and robustness of the learning algorithm. The memory learning term consists of two parts: and .in It is the memory information from the previous iteration cycle. It is a gain coefficient. This term provides historical inertia to the learning process, ensuring that current learning decisions are based not only on instantaneous information but also on historical experience, thus helping to smooth the learning process. For d-axis current The direct compensation term. Since the d-axis current is crucial in the field-oriented control of the PMSM and its dynamics are closely related to chaotic behavior, directly incorporating its historical values ​​into the learning term can compensate for its repetitive oscillations more quickly and directly. This is the weight of that item.

[0079] Directly using formulas Calculated results Let this be the initial feedforward compensation amount. It should be noted that directly adding the initial feedforward compensation amount to the control input without considering its amplitude is dangerous. An excessively large feedforward compensation amount may saturate the total control input depth, not only failing to achieve the expected learning effect but also potentially compromising the stability of the FASMC and even causing the system to diverge. Therefore, in this embodiment, an amplitude limit is imposed on the ILC learning term itself. Specifically, the amplitude limit function... Represented as: ; in, It is the first The maximum allowable amplitude of the ILC term during the next iteration.

[0080] In this embodiment, the maximum allowable amplitude of the amplitude limiting function With the number of iterations Gradual relaxation is represented as: ; In the formula, This indicates the upper limit of the maximum allowable amplitude of the feedforward compensation.

[0081] For example, a closed-loop system can provide [something] within the finite time domain of one iteration. t ∈[0,50].

[0082] Step 5: During each iteration, the feedback control quantity output by the fuzzy adaptive sliding mode controller is superimposed with the feedforward compensation quantity provided by the iterative learning controller for the current iteration to form the total control input applied to the permanent magnet synchronous motor.

[0083] In this embodiment, a sliding mode observer is used to obtain the state estimate in real time. The real-time state error is calculated based on the state estimate and the desired equilibrium point. The fuzzy adaptive sliding mode controller uses the control law to calculate the feedback control quantity based on the state error.

[0084] Step 6: After each iteration, using the tracking error of the current iteration, update the feedforward compensation amount for the next iteration according to the update law of the iterative learning controller, and enter the next iteration. Repeat steps 5 to 6 until the tracking error meets the preset accuracy requirements.

[0085] Understandably, during the first iteration, settings are made... The value is 0, and the closed-loop system is... During internal operation, FASMC calculates the feedback control quantity based on the state error using its control law. The total control input is After the operation is completed, the weighted tracking error is recorded. The feedforward compensation amount for the next iteration is calculated using the update law of ILC. .

[0086] During the second iteration, FASMC still calculates the feedback control quantity in real time. At the same time, the pre-calculated feedforward compensation amount Superimposed on the control input, i.e., the total control input is After the operation is completed, the weighted tracking error is recorded. Update feedforward compensation amount .

[0087] Similarly, steps 5 and 6 are repeated. As the number of iterations increases, the feedforward signal learned by the ILC gradually approaches the ideal compensation amount, and the tracking error decreases successively. This continues until the tracking error meets the specified condition. Stop iteration, where , This is the residual term introduced by modeling error, saturated nonlinearity, and incomplete repetitive perturbation. Therefore, the iteration error is uniformly and eventually bounded with respect to the iteration number k; when... When the system degenerates to the ideal repetitive task scenario, geometric convergence can be further obtained.

[0088] It is understood that the control flow of the PMSM chaotic control method of the integrated sliding mode observer of the present invention can be divided into four core stages: state observation, feedback control, feedforward learning, control quantity superposition and system driving. The specific flow is as follows: (1) State observation phase PMSM chaotic system outputs actual state signal This signal is input to the sliding mode observer. Based on the system dynamics model and the sliding mode variable structure control principle, the sliding mode observer estimates unmeasurable system states such as rotor angular velocity and winding current, and outputs state estimates. This provides reliable status feedback information for subsequent feedback control.

[0089] (2) Feedback control stage The expected input signal and the state estimate output by the sliding mode observer The input is then fed into FASMC. FASMC combines the adaptive capability of fuzzy logic with the robustness of sliding mode control to analyze the deviation between the desired input and the actual estimated state, generating a feedback control quantity. It is used to suppress system disturbances and track the desired trajectory in real time.

[0090] (3) Feedforward learning stage Output of PMSM chaotic system The expected input is fed into the error calculation module to obtain the error signal. The error signal is input to the ILC, which performs iterative learning based on historical error data to generate a feedforward compensation amount. It is used to compensate for periodic errors or repetitive disturbances in the system.

[0091] (4) Control quantity superposition and system driving stage FASMC generates feedback control quantity Feedforward compensation amount generated by ILC The inputs are summed in the overlay module to form the total control input. The total control input acts on the PMSM chaotic system, driving the system's operation and generating new outputs. This completes a closed-loop cycle of one control period. The entire process utilizes an integrated architecture that achieves state perception through a sliding mode observer, robust feedback through a FASMC, and feedforward learning compensation through an ILC. This enables high-precision and robust control of PMSM chaotic systems, while also possessing adaptive learning capabilities to cope with the complex characteristics of the system.

[0092] In this embodiment, the sliding mode observer, through its unique discontinuous feedback mechanism, provides a powerful theoretical tool for achieving high-precision and robust state estimation under conditions of model uncertainty and external disturbances. Introducing it into the PMSM chaotic control system solves the problem that key state variables such as rotor angular velocity and dq-axis current may not be directly or accurately measured, providing reliable state feedback information for subsequent fuzzy sliding mode controllers and iterative learning mechanisms, further enhancing its feasibility and robustness in practical applications.

[0093] The PMSM chaotic control method of the integrated sliding mode observer in this invention embodiment is based on T The sliding mode observer designed using the S-fuzzy model can quickly and accurately estimate unmeasurable states under parameter uncertainty and bounded disturbances, and simultaneously use the estimated values ​​for feedback control and iterative learning. This design reduces the system's dependence on physical sensors, improves engineering economy and reliability, and makes the invention applicable to practical operating conditions where states are not fully measurable. Through the sliding mode observer's ability to suppress lumped uncertainty terms, the online estimation of the disturbance upper bound of the fuzzy adaptive sliding mode controller, and the learning compensation for repetitive disturbances by iterative learning control, the system maintains excellent stability and consistency even under complex operating conditions where parameter perturbations, external disturbances, and measurement noise coexist.

[0094] Furthermore, the effectiveness of the PMSM chaotic control method of the integrated sliding mode observer in this embodiment is illustrated through simulation experiments.

[0095] System parameters are selected as follows , The initial state is set to [ , , ] = [0.01, 0.01, 0.01], the control objective is to stabilize the system to the equilibrium point. The system is subjected to a bounded external disturbance. The system is The controller is started at time s to compare the state reconstruction effects in scenarios with and without observers.

[0096] Please see Figure 5 and Figure 6 , Figure 5The figure shown is a comparison between the state estimate and the true value of the rotor angular velocity of the sliding mode observer; Figure 6 The figure shows a comparison between the state estimate and the actual value of the d-axis current of the sliding mode observer. The performance analysis results of the sliding mode observer during the control phase are shown in Table 1.

[0097] Table 1

[0098] from Figure 5 and Figure 6 As can be seen, the sliding mode observer can quickly track the true value and maintain consistency after a brief transient. The error converges to the ±5% error band within 0.43s and 0.90s, which is much lower than the chaotic oscillation period of the PMSM (approximately 2.1s). Table 1 shows that the RMSE of the rotor angular velocity is 0.25817, and the RMSE of the d-axis current is 0.124645, both significantly smaller than the dynamic range of the system. The maximum peak errors are 2.30 and 0.66, respectively, with durations both less than 0.05s.

[0099] The simulation results show that the SMO designed in this invention can achieve fast and error-bounded critical state estimation under the set operating conditions, providing usable state feedback information for the subsequent controller.

[0100] Furthermore, a corresponding modular simulation model was built based on the MATLAB / Simulink platform, and the system response characteristics were analyzed from both the time and frequency domains. Specifically, an integrated control architecture with coordinated state observation, feedforward learning, and feedback stabilization loops was constructed. The core idea of ​​this architecture lies in functional decoupling and spatiotemporal separation: the SMO provides estimates of key state variables in the continuous time domain, the ILC learns periodic feedforward compensation in the iterative batch domain, and the FASMC ensures system robustness in the real-time feedback loop.

[0101] From both time and frequency domain perspectives, the closed-loop performance of the following three control configurations is systematically compared and analyzed: ① No SMO - 1st iteration (FASMC only): as a performance benchmark; ② No SMO - 30th iteration (FASMC+ILC): Evaluate the learning effect of ILC; ③ With SMO - 30th iteration (FASMC+ILC+SMO): Demonstrates the superiority of the complete integrated solution.

[0102] To reduce the randomness of frequency domain indices under single-parameter conditions, a random perturbation of ±5% was applied to the system parameters in each Monte Carlo experiment, and local linearization was performed again in the neighborhood of the same equilibrium point. The corresponding open-loop frequency domain indices were then extracted, and the statistical results shown in Table 2 were obtained. The data format is "mean ± standard deviation", based on 30 Monte Carlo simulations.

[0103] Table 2

[0104] As shown in Table 2, the ILC-FASMC-SMO integrated scheme proposed in this invention exhibits the best frequency domain performance. Regarding phase margin, the increase of 7.19° indicates a greater time delay tolerance; the increase of 7.92dB in gain margin demonstrates the system's ability to tolerate larger open-loop gain variations and its stronger adaptability to parameter drift and modeling errors. The overall frequency characteristics extend towards higher frequencies, indicating a faster dynamic response potential in the equilibrium point neighborhood. The smaller standard deviations of each indicator suggest better consistency of the integrated scheme under parameter perturbations.

[0105] To further verify the integrated controller's ability to suppress measurement noise in practical engineering, this section introduces 10% amplitude white noise into the system output channel to simulate random interference commonly found in actual sensor measurements.

[0106] Please refer to the above. Figures 7-9 , Figure 7 The figure shown is a comparison of the rotor angular velocity response of the method of the present invention under white noise interference; Figure 8 The figure shown is a comparison of the d-axis current response of the method of the present invention under white noise interference; Figure 9 The figure shows a comparison of the q-axis current response of the method of the present invention under white noise interference. The blue curve represents the noise-free case, and the red curve represents the case with noise.

[0107] As shown in the figure, although the system response exhibits high-frequency jitter after the introduction of noise, the integrated controller can still quickly suppress the noise's influence. The rotor angular velocity converges to the steady-state band within 0.48s, indicating that the observer and controller have good filtering and suppression capabilities for noise. Noise mainly affects the high-frequency components of the current, but the system can still recover its stability within 0.45s, with current amplitude fluctuations effectively limited to within ±0.05A. This demonstrates that the boundary layer design of the sliding mode observer and the feedforward compensation mechanism of the ILC have a significant suppression effect on current loop noise. Similar to the d-axis current, the q-axis current exhibits slight flutter under noise excitation, but the system re-enters steady state within 0.42s, and the steady-state error is basically consistent with the noise-free case, further verifying the robustness of the integrated controller in the current loop.

[0108] To quantify the dynamic performance of the ILC-FASMC-SMO integrated control scheme in the time domain, the experimental conditions were set as follows: system parameters initial state External disturbances The control signal is applied at t=30s, and the system sampling period is set to... Please see. Figures 10-13 The figure shows a time-domain performance comparison of different control configurations (FASMC, ILC-FASMC, and the ILC-FASMC-SMO integrated scheme proposed in this invention only). Figure 10 A comparison of the time-domain response of rotor angular velocity under three control configurations. Figure 11 A comparison of the time-domain response of the q-axis current under three control configurations. Figure 12 A comparison of the time-domain response of the d-axis current under three control configurations. Figure 13 A comparison of the time-domain response of the control input under three control configurations.

[0109] As can be seen from the figure, the integrated scheme proposed in this invention outperforms the other two schemes in terms of speed, current, and control input response. To further quantify the performance differences between different control schemes and overcome the randomness of single simulation results, 30 Monte Carlo simulations were performed on each scheme. In each simulation, ±5% parameter perturbation and random seed noise were randomly added. The statistical results are shown in Table 3. The improvement rate was calculated based on the FASMC scheme.

[0110] Table 3

[0111] As shown in Table 3, the ILC-FASMC-SMO integrated scheme proposed in this invention outperforms the comparative schemes in all performance indicators. In terms of dynamic response, it reduces the dynamic response by 87.6% compared to the FASMC scheme; the speed convergence time is shortened by 58.4%. Regarding steady-state accuracy, the q-axis current RMSE is reduced by 37.8%, and the d-axis current RMSE is reduced by 49.1%. In terms of control quality, the peak voltage is reduced by 32.9%, and the number of saturation cycles is reduced by 87.2%. The standard deviations of all indicators are small, indicating that the proposed scheme has good consistency in results under multiple random disturbance tests; furthermore, it maintains excellent control performance under the combined effects of parameter perturbations and random noise, demonstrating strong robustness.

[0112] Combination Figures 10-13The time-domain response curves further demonstrate that the ILC-FASMC-SMO scheme can suppress chaotic oscillations more quickly after the controller is engaged and significantly improve the smoothness of speed and current responses. This indicates that, based on ILC feedforward compensation and FASMC feedback stabilization, the introduction of SMO can provide the controller with more accurate state information, thereby further improving the dynamic response quality and overall control performance of the system.

[0113] It should be noted that, in this document, relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations are intended to cover non-exclusive inclusion, such that an article or apparatus comprising a list of elements includes not only those elements but also other elements not expressly listed. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the article or apparatus that includes said element. Terms such as "connected" or "linked" are not limited to physical or mechanical connections but can include electrical connections, whether direct or indirect. The orientations or positional relationships indicated by terms such as "upper," "lower," "left," and "right" are based on the orientations or positional relationships shown in the accompanying drawings and are used only for the convenience of describing the invention and for simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be construed as limiting the invention.

[0114] In the description of this specification, the references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features or characteristics described may be combined in any suitable manner in one or more embodiments or examples. In addition, those skilled in the art can combine and integrate the different embodiments or examples described in this specification.

[0115] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A PMSM chaotic control method with an integrated sliding mode observer, characterized in that, include: Step 1: Establish a dimensionless chaotic dynamic model of the permanent magnet synchronous motor, construct a TS fuzzy model under parameter uncertainty based on the dimensionless chaotic dynamic model, and define the expected equilibrium point of the PMSM chaotic system; Step 2: Design a sliding mode observer based on the TS fuzzy model. The sliding mode observer is used to reconstruct the unmeasurable state variables online using the measurable output of the permanent magnet synchronous motor to obtain the state estimate. Step 3: Based on the TS fuzzy model, design a fuzzy adaptive sliding mode controller to form a feedback stabilization loop and a closed-loop system. The fuzzy adaptive sliding mode controller is used to generate feedback control quantity to suppress non-repetitive disturbances based on the state error calculated from the state estimate and the desired equilibrium point. Step 4: Design an iterative learning controller to form a feedforward control loop, so as to learn the repeatable residual error of the closed-loop system in the finite time domain during one iteration and generate the feedforward compensation quantity. Step 5: During each iteration, the feedback control quantity output by the fuzzy adaptive sliding mode controller is superimposed with the feedforward compensation quantity provided by the iterative learning controller for the current iteration to form a total control input applied to the permanent magnet synchronous motor. Step 6: After each iteration, using the tracking error of the current iteration, update the feedforward compensation amount for the next iteration according to the update law of the iterative learning controller, and enter the next iteration. Repeat steps 5 to 6 until the tracking error meets the preset accuracy requirements.

2. The PMSM chaotic control method with an integrated sliding mode observer according to claim 1, characterized in that, Step 1 includes: Step 1.1: Establish a dimensionless chaotic dynamic model of the permanent magnet synchronous motor in the dq-axis coordinate system; Step 1.2: Using the state variables of the permanent magnet synchronous motor as fuzzy antecedents, set the fuzzy set and membership function, represent the dimensionless chaotic dynamics model as a weighted combination of several local linear subsystems, and introduce internal parameter disturbances and bounded external disturbances to obtain the TS fuzzy model, and define the desired equilibrium point of the PMSM chaotic system.

3. The PMSM chaotic control method with an integrated sliding mode observer according to claim 2, characterized in that, The TS fuzzy model is represented as follows: ； in, Let be the system state vector. For the system's control input, For the first The state matrix corresponding to the fuzzy rules, For the input matrix, For the parameter uncertainty term, For a bounded external disturbance, satisfying , This represents the upper bound function of the perturbation. Indicates time, This is the normalized membership function.

4. The PMSM chaotic control method with an integrated sliding mode observer according to claim 1, characterized in that, Step 2, which involves designing a sliding mode observer, includes: S11: Construct a sliding mode observer structure corresponding to the fuzzy rules of the TS fuzzy model, expressed as: ； in, This is the state estimate. Let be the input vector of the system, and let be the first... The state matrix corresponding to the fuzzy rules, For the input matrix, Indicates time, For the normalized membership function, For fuzzy reasoning input, It is the first i The linear observer gain matrix corresponding to the fuzzy rule. For system output, To output the estimated value, For the first i The sliding switch item corresponding to the fuzzy rule; S12: Define the state estimation error and determine the dynamic equation of the state estimation error based on the TS fuzzy model and the sliding mode observer structure; S13: Construct a sliding surface based on the output estimation error, and design a sliding mode switching term based on the sliding surface to suppress observer chattering.

5. The PMSM chaotic control method with an integrated sliding mode observer according to claim 4, characterized in that, No. i The sliding switch term corresponding to each fuzzy rule is represented as: In the formula, To switch the gain, a matrix is ​​designed for the sliding surface. For the output matrix, It is a positive definite matrix. Boundary layer thickness, It is a sliding surface.

6. The PMSM chaotic control method with an integrated sliding mode observer according to claim 1, characterized in that, Step 3, which involves designing a fuzzy adaptive sliding mode controller, includes: S21: The fractional-order sliding surface is designed as follows: ； in, It is a fractional-order sliding surface. For time, For rotor angular velocity error, For d-axis current error, For q-axis current error, The fractional-order gain coefficient, The linear gain coefficient, and , It is a fractional power, and ; S22: Design a control law based on the fractional-order sliding surface. The control law is expressed as follows: ； In the formula, This is an equivalent control law. To switch control laws; The equivalent control law is expressed as follows: ； In the formula, For system state-related functions; The switching control law is expressed as follows: ； In the formula, To switch the gain, It is a fractional-order sliding surface. It is a saturation function. Boundary thickness; S23: A fuzzy logic system is used to adjust the switching gain of the switching control law in real time to achieve adaptive chattering suppression.

7. The PMSM chaotic control method with an integrated sliding mode observer according to claim 6, characterized in that, The method for updating the switching gain is as follows: ； In the formula, Based on the gain, The switching gain adjustment amount is the output of the fuzzy logic system. For fuzzy output scaling factor, For adaptive learning rate, For, a fractional-order sliding surface.

8. The PMSM chaotic control method with an integrated sliding mode observer according to claim 1, characterized in that, Step 4 involves designing an iterative learning controller, including: S31: The weighted tracking error is constructed as follows: ； In the formula, For weighted tracking error, For the number of iterations, For time, The rotor angular velocity, For d-axis current, For q-axis current, This is the weighting coefficient for the rotor angular velocity. This is the weighting coefficient for the d-axis current. This is the weighting coefficient for the q-axis current; S32: Design the update law of the iterative learning controller based on the weighted tracking error, the update law being expressed as: ； In the formula, For the first Feedforward compensation amount in the next iteration. For learning rate, For the derivative term of the weighted tracking error, For gain coefficient, For the first The memory information of the next iteration This is an amplitude limiting function. These are the weighting coefficients. For the axis current.

9. The PMSM chaotic control method with an integrated sliding mode observer according to claim 8, characterized in that, The learning rate An adaptive mechanism is used, which is expressed as: ； In the formula, Based on learning rate decay, The value varies with the number of iterations The increase is monotonically decreasing. For error trend factor, The value is adjusted in real time based on the changing trend of the weighted tracking error within a preset short time window. This is the weighted tracking error.

10. The PMSM chaotic control method with an integrated sliding mode observer according to claim 8, characterized in that, The maximum allowable amplitude of the amplitude limiting function varies with the number of iterations. Gradual relaxation is represented as: ； In the formula, This indicates the upper limit of the maximum allowable amplitude of the feedforward compensation.

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